[Reprinted  from  the  Physical  Review,  Vol.  XI.,  No.  i,  July,  1900.] 


ELECTRICAL  RESISTANCE  OF  THIN  FILMS  DE- 
POSITED BY  KATHODE  DISCHARGE. 

By  A C.  Longden, 

Introduction. 

IF  standard  high  resistances  of  great  precision  and  unvarying 
values  could  be  obtained  at  low  cost,  their  application  in  the 
determination  of  insulation  resistance  by  the  direct  deflection 
method  would  soon  cease  to  be  their  sole  field  of  general  use- 
fulness. The  condenser  and  ballistic  galvanometer  would  no  longer 
be  regarded  as  important  or  even  desirable  in  comparing  electro- 
motive forces,  and  a high  resistance  could  even  be  used  with  some 
advantage  in  place  of  a condenser,  in  the  condenser  method,  for 
measuring  internal  battery  resistance. 

The  use  of  numerous  shunts  in  the  determination  of  figure  of 
merit  is  always  regarded  as  something  to  be  endured  rather  than 
desired.  With  a suitable  high  resistance  in  series  with  the  galva- 
nometer and  standard  cell,  the  determination  of  figure  of  merit  be- 
comes absolutely  simple.  The  range  of  the  Wheatstone  bridge 
may  also  be  enormously  increased  by  the  use  of  high  resistances  as 
bridge  arms,  and  heavy  currents  may  be  measured  with  delicate 
galvanometers  in  series  with  high  resistances,  without  making  the 
resistance  of  the  shunt  through  which  the  main  current  passes  so 
small  that  the  percentage  of  error  in  the  calculations  shall  be  large. 

The  use  of  carbon  as  a high  resistance  material  is  tolerably  sat- 
isfactory for  some  purposes,  if  we  are  willing  to  re-standardize  our 
resistances  every  time  we  use  them,  and  to  reckon  with  the  enor- 
mously high  temperature  coefficient  of  the  material ; even  then,  the 
uncertainty  of  the  contacts  in  most  forms  of  carbon  resistances  is 
so  great  as  to  condemn  such  resistances  in  all  cases  where  anything 
like  careful  or  accurate  work  is  contemplated. 

A number  of  forms  of  carbon  resistances  have  been  used  in  con- 
nection with  the  research  which  furnishes  the  subject  matter  of  this 


41 


A.  C.  LONG  DEN. 


[Vol.  XI. 


article.  It  would  not  be  in  place  to  give  detailed  descriptions  of 
them  here,  but  it  may  be  well  to  say  in  passing,  that  those  which 
were  the  most  nearly  trustworthy  consisted  of  sticks  of  pipe  clay 
saturated  with  sugar  solutions,  of  different  degrees  of  concentration 
— the  sugar  being  subsequently  carbonized  in  the  sticks  by  con- 
tinued exposure  to  a red  heat,  in  the  absence  of  oxygen.  The  re- 
sistance of  the  stick  depends  upon  the  degree  of  concentration  of 
the  sugar  solution  used  in  preparing  it. 

While  these  resistances  were  very  satisfactory  for  carbon,  it  must 
still  be  said  that  no  carbon  resistance  can  be  considered  for  a mo- 
ment in  comparison  with  standard  wire  resistances. 

In  wire  resistances,  the  use  of  alloys  instead  of  pure  metals  is 
based  upon  the  fact  that  alloys  have,  in  general,  lower  temperature 
coefficients  and  higher  specific  resistance  than  pure  metals  ; but  it 
must  be  borne  in  mind  that,  so  far  as  high  specific  resistance  is  con- 
cerned, it  is  not  in  itself  an  advantage,  but  is  only  a means  to  an 
end.  A wire,  having  a high  specific  resistance,  enables  us  to  obtain 
a high  resistance,  having  small  weight,  small  bulk  and  compara- 
tively low  cost.  If  these  conditions  could  be  met  as  well  or  better 
in  some  other  way,  high  specific  resistance  would  be  of  no  impor- 
tance whatever. 

Alloys  are  certainly  inferior  to  pure  metals  in  some  respects. 
Aside  from  the  molecular  rearrangement  which  may  be  going  on  in 
either  the  alloy  or  pure  metal,  alloys  suffer  from  disintegration  and 
possibly  from  internal  chemical  changes  which  are  impossible  in 
pure  metals.  It  is  also  true  that  alloys  frequently  suffer  from  con- 
tact with  their  surroundings.  Manganin,  for  example,  is  very  easily 
oxidized,  and  is  even  pronounced  by  some  investigators  as  worthless. 
Among  the  pure  metals  there  are  several  which  resist  oxidation  and 
other  chemical  changes  admirably.  Now  if  it  is  possible  to  obtain 
a high  resistance  in  the  form  of  a pure  metal,  and  at  the  same  time 
to  retain  all  the  advantages  of  an  alloy,  such  a resistance  ought  to 
soon  find  favor  in  the  electrical  world. 

From  the  results  of  some  work  done  a few  years  since  by  Miss 
Isabelle  Stone,1  we  have  reason  to  believe  that  metals  in  the  form  of 

1 “ On  the  Electrical  Resistance  of  Thin  Films,”  Physical  Review,  Vol.  6,  pp. 


No.  i.] 


RESISTANCE  OF  THIN  FILMS . 


42 


thin  films  upon  glass  exhibit  certain  qualities  unlike  those  of  the 
same  metals  in  the  ordinary  form.  Miss  Stone  reached  three  con- 
clusions, which  may  be  stated  as  follows  : 

1.  The  electrical  resistance  of  such  films  as  she  investigated  de- 
creases in  value  quite  rapidly  for  a short  time,  then  less  rapidly  for 
a much  longer  time. 

2.  The  higher  the  resistance  of  the  film,  the  more  rapid  is  the 
decrease  in  value. 

3.  For  very  thin  films,  the  ratio  of  the  measured  resistance  to  the 
calculated  resistance  is  high. 

Miss  Stone’s  research  included  silver  films  only,  and  these  were 
deposited  from  aqueous  solutions  by  what  is  known  as  the  Rochelle 
salt  method  ; but  her  work  is  suggestive  of  a very  large  field  of 
research,  if  other  methods  of  deposition  could  be  used. 

As  early  as  1877  Professor  A.  W.  Wright1  of  Yale,  described  a 
method  of  depositing  thin  metallic  films  upon  glass  by  electrical 
discharge.  Professor  Wright  produced  both  opaque  and  transparent 
mirrors  from  a large  number  of  metals,  pointed  out  the  difference 
in  rate  of  deposition  of  different  metals,  and  suggested  that  on  ac- 
count of  the  difficulty  of  depositing  aluminum  and  magnesium,  these 
metals  should  be  used  for  electrodes  in  vacuum  tubes  in  order  to 
5 avoid  the  discoloration  so  common  in  the  neighborhood  of  the 
kathode  when  platinum  electrodes  are  employed. 

About  two  and  a half  years  ago  it  was  my  good  fortune  to  learn 
--0  the  practical  details  of  Professor  Wright’s  process  in  Ryerson  Phys- 
J ical  Laboratory  at  the  University  of  Chicago  ; and  to  have  the  op- 
portunity  of  preparing  a number  of  mirrors  and  thin  metallic  films, 
with  the  admirable  apparatus  designed  for  this  purpose  by  Professor 
Stratton  and  Dr.  Mann,  of  that  institution. 

Deposition  of  Films. 

The  deposition  is  effected  in  a vacuum,  by  a process  which  may 
here  be  included  for  convenience  under  the  general  term  kathode 

1 “ On  the  Production  of  Transparent  Metallic  Films  by  the  Electrical  Discharge  in 
Exhausted  Tubes,”  Am.  Journal  of  Science  and  Arts,  Vol.  13,  pp.  49-55. 

“On  a New  Process  for  the  Electrical  Deposition  of  Metals  and  for  Constructing 
Metal-Covered  Glass  Specula,”  Am.  Journal  of  Science  and  Arts,  Vol.  14,  pp.  169-178. 


43 


A.  C.  LONG  DEN. 


[Vol.  XI. 


discharge,1  from  an  electrode  consisting  of  the  metal  to  be  de- 
posited. 

The  necessary  apparatus  for  doing  the  work  advantageously  in- 
cludes a vacuum  pump  capable  of  reducing  the  pressure  in  the  re- 
ceiver to  a few  millionths  of  an  atmosphere ; an  induction  coil 
capable  of  producing  a spark  eight  or  ten  centimeters  long ; an  in- 
terrupter making  a complete  break  in  the  circuit,  and  preferably 
of  high  frequency ; and  a source  of  electrical  energy,  capable  of 
furnishing  a current  of  several  amperes,  at  a pressure  of  not  less 
than  fifty  volts,  if  the  Wehnelt  interrupter  is  used. 

The  pump  used  in  the  part  of  the  work  done  in  Chicago  was  a 
double  acting  Geissler  pump,  all  glass,  and  exhausting  into  a very 
good  secondary  vacuum  at  each  end  of  the  stroke,  so  that  the  mer- 
cury in  the  main  pump  was  never  in  contact  with  the  air.  This 
pump  is  capable  of  producing  a splendid  vacuum,  but  must  be 
rather  carefully  handled,  as  the  tendency  to  develop  leaks  is  some- 
what aggravated  by  the  fact  that  the  entire  apparatus  is  in  continual 
motion  when  in  use. 

In  continuing  the  work  at  Columbia  University,  it  seemed  desir- 
able to  construct  a pump  which  should  be  free  from  constant  danger 
of  developing  leaks,  and  which  should  be  capable  of  producing  the 
required  vacuum  rapidly  and  easily.  The  Sprengel  pump  is  slow, 
and  the  ordinary  Geissler  pump  with  its  numerous  ground  joints, 
valves  and  stop-cocks,  and  its  rubber  connecting  tube,  is  a little  un- 
certain, and  at  best,  somewhat  less  effective  than  the  necessities  of 
this  case  require.  A Geissler  pump  was  finally  decided  upon,  but 
not  without  a determination  to  eliminate  some  of  its  objectionable 
features. 

Figure  i shows  a diagram  of  the  working  parts.  The  right-hand 
side  of  the  pump,  as  viewed  in  the  diagram,  is  in  some  respects  sim- 
ilar to  the  Bessel-Hagen  2 pump,  but  simpler.  The  tube  ( A ) lead- 
ing from  the  exhaust  chamber  to  the  receiver  rises  to  the  height  of 
a full  meter  above  the  level  of  the  mercury  at  ( B ),  when  the  reser- 
voir (C)  is  elevated.  This  feature  of  the  apparatus  is  used  instead 

1 The  nature  of  the  process  will  be  considered  more  in  detail  hereafter. 

2 “ Ueber  eine  Neue  Form  der  Toepler’schen  Quecksilberluftpumpe  und  einige  mit 
ihr  angestellte  Versuche,”  Wied.  Ann.,  Vol.  12,  pp.  425-445. 


No.  i.] 


RESISTANCE  OF  THIN  FILMS. 


44 


of  a valve  to  prevent  the  flow  of  mercury  from  the  exhaust  chamber 
( D ) to  the  receiver.  As  the  mercury  sometimes  rises  in  this  tube 
with  considerable  momentum,  it  reaches  a point  considerably  above 
barometric  height,  but  the  bulb  (A),  two  or 
three  centimeters  in  diameter,  arrests  any  un- 
usually active  mercury  which  might  otherwise 
pass  around  the  bend  at  the  top  of  the  tube. 
The  tube  (A)  completes  the  passage  to  the 
receiver,  by  way  of  the  drying  chamber  ( G ), 
which  is  sealed  on  with  the  blow-pipe.  There 
are  no  ground  joints  or  even  mercury  seals  in 
any  part  of  the  apparatus. 

The  tube  (H)  is  a capillary  through  which 
air  may  be  gradually  admitted  when  the  re- 
ceiver is  to  be  opened.  The  tube  (A")  leads  to 
the  McLeod  gauge  (A).  The  reservoir  (M) 
is  for  the  purpose  of  filling  the  McLeod  gauge. 
Before  beginning  to  exhaust,  the  mercury  in 
the  gauge  tube  stands  at  (A),  at  the  same 
level  as  the  mercury  in  the  cistern  of  an  in- 
dependent barometer  (A).  As  the  exhaustion 
proceeds  the  mercury  rises  in  the  tube  (A) 
until  it  stands  at  (5),  the  level  of  the  mercury 
in  the  independent  barometer.  Of  course  the  tube  (A)  answers 
the  purpose  of  a gauge  until  the  mercury  rises  so  high  that  the 
difference  between  the  two  mercury  columns  is  not  easily  readable. 
After  this  the  McLeod  gauge  is  used. 

The  rubber  tube  which  usually  connects  the  reservoir  with  the 
exhaust  chamber  in  the  Geissler  pump  is  entirely  displaced  in  this 
case,  by  an  iron  pipe  with  a swinging  joint.  This  improvement 
originated  with  Professor  Wm.  Hallock,  of  Columbia.  The  glass 
tube  (A)  extends  downward  from  the  exhaust  chamber  as  far  as  ( V), 
where  it  is  securely  cemented  into  an  enlargement  on  the  iron  pipe. 
From  this  point  on  to  the  reservoir  (C)  the  mercury  passage  con- 
sists entirely  of  iron  pipe.  The  swinging  joint  (IV)  is  a carefully 
selected  pipe  union  with  well  polished  bearing  surfaces  moving 
upon  a leather  washer.  The  reservoir  is  raised  and  lowered  by 


Wt 

A 


Fig.  1. 


45 


A.  C.  LONG  DEN. 


[Vol.  XI. 


simply  swinging  the  pipe,  and  the  rubber  tube  is  thus  entirely 
eliminated. 

This  pump  has  now  been  in  use  several  months,  and  its  behavior 
is  most  thoroughly  satisfactory.  Entire  freedom  from  danger  of  leaks 
is  a source  of  inestimable  satisfaction  in  work  of  this  kind.  The  re- 
sults obtained  are  so  uniform  that,  as  long  as  the  same  receiver  is 
used,  it  is  easy  to  tell  before  beginning  an  operation,  just  how  many 
strokes  will  be  necessary  to  produce  a certain  degree  of  attenuation 
in  the  receiver.  So  confidently  can  this  uniformity  of  results  be  re- 
lied upon  that  the  McLeod  gauge  has  become  almost  unnecessary. 

The  exact  degree  of  exhaustion  which  this  pump  is  capable  of 
producing  has  not  been  carefully  determined,  because  it  has  not 
been  necessary  to  push  it  to  its  limit ; but  the  fact  that  a pressure  of 
one  hundred  thousandth  of  an  atmosphere  may  be  reached  with  ex- 
treme ease  and  certainty  is  evidence  that  the  limit  of  usefulness  of 
the  pump  has  not  been  approached. 

Notwithstanding  the  fact  that  this  pump  is  single-acting  and  open 
to  the  air  at  one  end  of  the  stroke,  the  necessary  vacuum  for  the 
deposition  of  metals  can  be  produced  with  it  in  less  than  half  the 
time  required  for  the  same  operation  with  the  double-acting  pump 
already  referred  to. 

The  induction  coil  used  in  the  earlier  experiments  was  a large 
one,  capable  of  producing  a 30-cm.  spark  in  air.  The  coil  used 
later  was  not  more  than  half  as  large  ; but  a coil  half  the  size  of 
either  of  them  would  be  abundantly  large  for  the  purpose. 

The  current  interrupter  used  in  the  early  part  of  the  work  was  a 
mechanical  interrupter  operated  by  an  electric  motor  in  a separate 
circuit.  The  speed  of  the  motor  was  usually  about  1,500  revolu- 
tions per  minute,  with  two  breaks  per  revolution.  This  was  quite 
satisfactory  except  that  the  deposition  of  metal  would  have  been  more 
rapid  with  an  interrupter  of  greater  frequency.  The  Wehnelt  in- 
terrupter 1 is  so  well  suited  to  this  work  that  no  other  has  been 
used  since  its  advent. 

The  receiver  in  which  the  films  are  deposited  is  represented  in  ver- 
tical section  in  figure  2.  (TM),  figure  2,  is  a rubber  stopper  through 

which  a glass  tube  ( B ) enters  the  receiver.  This  tube  serves  at 
1 Elektrotechnische  Zeitschrift,  Vol.  20,  pp.  76-78. 


No.  i.] 


RESISTAXCE  OF  THEY  FILMS. 


46 


SCALE  OF  CENTIMETERS 


once  as  an  exhaust  tube  and  as  a passage  way  for  the  kathode  wire 
( C ).  The  tube  and  stopper  are  securely  cemented  into  the  open 
top  of  the  receiver,  with  sealing  wax  ( DDDD ).  The  lower 

end  of  the  kathode  wire  terminates  in 
a thin  aluminum  tube,  just  large  enough 
to  drive  firmly  into  the  lower  end  of 
the  glass  tube  ( B ).  The  kathode  plate 
(. E ) which  consists  of  the  metal  to  be 
deposited,  is  supported  by  an  aluminum 
rod  (F),  which  slides  into  the  thin 
aluminum  tube  with  just  enough  friction 
to. hold  it  in  place.  ( G ) is  a heavy 
aluminum  base  plate,  which  serves  as 
the  anode,  and  (//)  is  an  additional 
aluminum  plate,  which  serves  as  a sup- 
port for  the  glass  plate  (Z),  upon  the 
upper  surface  of  which  the  film  is  to 
be  deposited.  The  dimensions  may  be 
taken  from  the  figure  as  it  is  drawn 
to  scale. 

When  the  air  is  exhausted  from  the  receiver  and  discharges  from 
the  kathode  of  an  induction  coil  take  place  from  the  surface  of  (Z), 
particles  of  the  kathode  plate  (Z)  are  deposited  in  the  form  of  a 
brilliant  film  upon  the  surface  of  the  glass  plate  (Z)  and,  in  fact 
upon  the  entire  inner  surface  of  the  receiver. 

The  character  of  the  film  depends  largely  upon  the  rate  of  dep- 
osition, and  this  in  turn  depends  upon  the  vacuum,  the  electro- 
motive force,  the  current,  the  frequency  of  the  interrupter  and  the 
distance  from  the  kathode  to  the  glass  plate  upon  which  the  film  is 
to  be  deposited.  If  all  the  conditions  are  properly  adj  usted,  moder- 
ately rapid  deposition  will  produce  films  of  great  hardness,  density 
and  brilliancy.  If  the  deposition  is  too  rapid,  the  resulting  films 
will  possess  these  qualities  in  less  degree. 

The  factors  which  have  been  enumerated  as  affecting  the  rate  of 
deposition  are  so  intimately  related,  and  so  dependent  upon  each 
other,  that  it  is  quite  impossible  to  discuss  them  independently. 
Professor  Wright  produced  beautiful  mirrors  from  a very  small 


Fig.  2. 


47 


A.  C.  LONG  DEN. 


[VOL,  XI. 


kathode  in  a 2 mm.  vacuum  at  a 3 mm.  distance  with  a primary 
electro-motive  force  of  perhaps  a dozen  volts,  but  in  order  to  obtain 
an  even  distribution  of  metal  over  any  very  considerable  surface,  he 
found  it  necessary  to  keep  the  kathode  moving  over  the  surface 
during^the  process  of  deposition.  It  is  just  as  easy  to  obtain  an 
even  distribution  of  metal  over  a large  surface  from  a stationary 
kathode  by  using  a correspondingly  large  kathode  and  placing  it  at 
a large  distance  from  the  glass.  This,  however,  involves  working 
in  a higher  vacuum  and  using  a higher  electro-motive  force  ; and  in 
order  that  the  process  may  be  as  rapid,  it  necessitates  using  either 
a stronger  current  or  a higher  interruption  frequency.  A glass  sur- 
face 5x6  centimeters  may  be  beautifully  platinized  by  placing  it  at 
a distance  of  12  or  15  millimeters  from  a kathode  plate  of  similar 
dimensions,  in  a vacuum  of  from  .0001  to  .00001  of  an  atmosphere, 
and  operating  with  a primary  current  of  5 or  6 amperes  at  1 10 
volts,  and  with  an  interrupter  frequency  of  about  300  per  second. 

The  two  factors,  vacuum  and  distance,  are  related  to  each  other 
in  a way  which  demands  a more  detailed  consideration.  With  a 
certain  fixed  vacuum,  if  the  distance  from  the  kathode  to  the  glass 
plate  is  much  too  great,  the  film  will  be  soft  and  spongy ; while  if 


Fig.  3. 

the  distance  is  much  too  small  it  is  almost  impossible  to  get  any 
metal  deposited  at  all.  It  is  found  by  experiment  that  the  golden 
mean  between  these  two  extreme  conditions  is  attained  when  the 
surface  of  the  glass  plate  is  just  about  in  the  plane  which  marks  the 


No.  i.] 


RESISTANCE  OF  THIN  FILMS. 


48 


boundary  between  the  kathode  space  and  the  luminous  glow  which 
surrounds  it.  (See  figure  3.)  Films  deposited  at  other  positions 
vary  very  greatly  in  hardness  and  density.  Some  platinum  films 
will  scarcely  endure  the  touch  of  a camel’s  hair  brush,  while  others 
can  scarcely  be  removed  from  the  glass  by  the  most  vigorous  rub- 
bing, or  by  the  action  of  hot  aqua  regia. 

At  the  suggestion  of  Professor  Rood  an  attempt  was  made  to 
discover  the  condition  of  the  metal  during  its  transition  through  the 
kathode  space.  A glass  plate  5x6  centimeters,  was  placed  at  the 
usual  distance,  about  1 5 mm.  from  the  kathode.  In  the  center  of 
this  plate  was  placed  a small  aluminum  stand,  supporting  a small 
glass  plate  about  1 2 millimeters  square,  within  3 mm.  of  the  kath- 


Fig.  4. 


ode,  as  in  Fig.  4.  The  air  was  then  removed  from  the  receiver  until 
the  kathode  space  just  reached  the  surface  of  the  large  glass  plate 
(A).  A platinum  film  of  considerable  thickness  was  then  deposited. 
When  the  plates  were  removed  from  the  receiver,  it  was  found,  first 
that  the  film  on  the  upper  surface  of  the  small  plate  ( B ) was  exceed- 
ingly thin  ; next,  that  the  stand  had  not  cast  a distinct  shadow,  but 
that  the  film  on  the  large  plate  under  the  stand  gradually  shaded 
off  to  a comparatively  thin  center,  as  if  the  particles  of  platinum  had 
drifted  under  the  stand  in  considerable  quantities.  The  third  and 
most  surprising  fact  to  be  noted  was  that  the  unprotected  corners 
of  the  small  plate  were  quite  heavily  coated  on  the  under  side. 

In  the  light  of  these  facts  there  can  scarcely  be  any  doubt  in  re- 
gard to  the  nature  of  the  process.  The  surface  of  the  kathode  is 


49 


A.  C.  LONG  DEN. 


[Vol.  XI. 


4 


4 


intensely  heated,  and  particles,  probably  molecules,  possibly  smaller 
particles,1  are  projected  into  space.  These  particles  radiate  from 
the  kathode  in  the  gaseous  form  until  they  reach  the  limit  of  what 
is  called  the  kathode  space.  In  other  words  the  kathode  space  is 
the  space  in  which  the  metallic  matter  radiated  from  the  kathode  is 
still  in  the  gaseous  state.  When  the  temperature  has  fallen  to  a 
sufficient  degree,  condensation  begins,  and  we  have  the  visible  glow 
just  outside  the  kathode  space — a miniature  snow-storm. 

The  very  hot  metallic  gas  near  the  kathode  will  not  easily  adhere 
to  and  condense  upon  the  glass,  and  the  comparatively  cool  “vapor” 
if  we  may  use  the  term,  condenses  in  rather  a loose,  soft,  spongy 
layer.  It  is  on  this  account  that  the  best  mirrors  are  formed  just 
in  the  edge  of  the  kathode  space,  as  described  on  page  47. 

This  view  is  supported  by  the  fact  that  the  visible  glow  rises  to 
the  edge  of  the  small  stand  as  represented  at  (C),  in  figure  4.  The 
metallic  gas  flowing  over  the  surface  of  the  stand  is  cooled  some- 
what, and  the  snow-storm  therefore  begins  at  a shorter  distance 
from  the  kathode  in  this  region  than  in  the  free  space  in  the  other 
parts  of  the  receiver.  Further  evidence  is  offered  in  the  fact  that 
the  glow  around  the  stand  is  more  conspicuous  at  first  than  it  is 
after  the  stand  itself  has  become  somewhat  heated. 

The  process  seems  to  be  simple  distillation,  in  which  the  vaporiza- 
tion of  the  kathode  depends  largely  upon  its  electrification.2  That 
the  process  is  not  entirely  dependent  upon  electrification,  however,  is 
evident  from  the  fact  that  selenium,  which  boils  at  about  700  de- 
grees, is  deposited  thousands  of  times  more  rapidly  than  platinum. 

It  is  a noteworthy  fact  that  when  a rectangular  kathode  is  used 
in  a cylindrical  receiver,  the  deposit  on  the  sides  of  the  receiver  is 
thickest  at  small  areas  opposite  the  corners  of  the  kathode.  This 
is  not  because  the  distance  is  less,  but  because  the  surface  density 
of  the  charge  is  greater  at  these  points. 

1 J.  J.  Thompson,  in  Phil.  Mag.,  Dec.,  1899,  “ On  the  Masses  of  the  Ions  in  Gases  at 
Low  Pressures,”  says  that  incase  of  the  stream  of  negative  electrification  which  constitutes 
the  kathode  rays,  there  are  reasons  for  thinking  that  the  charge  on  the  ion  is  not  greatly 
different  from  the  electrolytic  one,  and  that  in  the  former  case  we  have  to  deal  with  masses 
smaller  than  the  atom. 

2 See  Sir  WiiliamCrookes  “ On  Electrical  Evaporation,”  Electrical  Review,  Vol.  28, 
pp.  796-798  and  827,  82S. 


No.  i.] 


RESISTANCE  OF  THIN  FILMS. 


50 


In  conducting  this  process,  it  is  not  an  easy  matter  to  keep  the 
vacuum  at  a fixed  value  during  the  first  part  of  the  experiment. 
When  the  circuit  is  first  closed,  the  effect  is  to  drive  off  the  residual 
air  and  occluded  gases.  This  produces  a change  of  pressure  in 
the  receiver,  which  is  quite  rapid  at  first,  but  less  and  less  rapid  as 
the  process  continues.  The  rate  at  which  the  first  change  takes 
place  depends  largely  upon  the  nature  of  the  kathode,  the  condi- 
tion of  the  atmosphere  to  which  it  has  been  exposed  and  the 
length  of  the  exposure. 

Under  what  might  be  called  ordinary  conditions,  when  a platinum 
kathode  is  used,  it  is  not  well  to  allow  the  current  to  continue  more 
than  a few  seconds  when  first  turned  on,  without  stopping  to  ob- 
serve the  condition  of  the  vacuum.  If  the  vacuum  is  allowed  to 
fall  below  .0001  of  an  atmosphere1  there  is  danger  of  the  film  be- 
ing rather  soft.  The  film  in  this  condition  will  not  adhere  well  to 
the  glass.  Hence  the  importance  of  being  particularly  careful 
about  the  vacuum  at  first. 

The  curves  ( A ) (. B ) and  (C)  in  figure  5,  represent  the  rate  of  de- 
terioration of  the  vacuum  during  the  rapid  part  of  its  change.  The 
vertical  portions  of  the  curves  represent  intervals  during  which  the 
coil  is  not  in  operation,  but  the  pump  is  being  used  to  improve  the 
vacuum.  These  curves  are  all  three  for  platinum  films.  Curve  ( A ) 
represents  an  extreme  case  in  which,  after  depositing  a film,  the  re- 
ceiver had  been  quickly  opened,  the  film  removed,  new  glass  in- 
serted and  the  receiver  again  sealed  and  exhausted — all  within  a few 
minutes.  Curve  ( C ) represents  another  extreme  case  in  which  both 
the  kathode  and  the  inside  of  the  receiver  had  been  exposed  to  the 
air  for  a long  time  and  under  very  unfavorable  conditions.  Curve 
( B ) may  be  said  to  fairly  represent  the  deterioration  of  the  vacuum 
during  the  first  ten  minutes  of  the  process  under  average  condi- 
tions. It  must  be  understood  that  in  all  these  cases,  the  minutes 
represented  on  the  axis  of  abscissae  are  not  consecutive  minutes, 
but  minutes  during  which  the  process  of  deposition  is  actually  go- 
ing on. 

Usually  after  ten  or  fifteen  minutes  of  actual  deposition , the  con- 
dition of  the  vacuum  does  not  change  much  and  the  deposition 

1 With  the  distance,  voltage,  etc.,  as  stated  on  page  47. 


5 1 


A.  C.  LONG  DEN. 


[VOL.  XI. 


i 


may  then  go  on  continuously  if  the  strength  of  the  current  used  is 
not  such  as  to  heat  the  receiver  excessively.  After  this  stage  has 
been  reached,  if  the  process  is  discontinued  for  half  an  hour  or  so, 
if  there  has  been  no  perceptible  leakage,  the  vacuum  is  found  to 


Fig.  5. 


have  improved  considerably  on  account  of  the  fact  that  most  of  the 
residual  gas  in  the  receiver  has  been  occluded  by  the  kathode  and 
film.  If  the  current  be  again  started,  however,  the  vacuum  will 
soon  fall  to  about  its  normal  value. 

Electrical  Properties  of  Films. 

Besides  possessing  splendid  reflecting  surfaces,  such  as  commend 
them  strongly  for  all  high  grade  optical  work,  and  besides  display- 
ing the  colors  of  the  different  metals  by  transmitted  light,  and  the 
selective  absorption  of  different  thicknesses  of  the  same  film,  metallic 
films  deposited  in  accordance  with  the  method  here  described  pos- 
sess certain  advantages  as  electrical  resistances. 

Without  an  exact  method  of  determining  the  thickness  of  a film 
it  is  impossible  to  make  an  exact  estimate  of  its  specific  resistance  ; 
but  even  with  only  an  approximate  determination  of  thickness,  the 


No.  i.] 


RESISTANCE  OF  THIN  FILMS. 


52 


very  rapid  increase  in  resistance  corresponding  to  diminishing  thick- 
ness is  so  conspicuous  as  to  leave  no  room  for  doubt  that  in  thin 
films  the  ratio  of  the  measured  resistance  to  the  calculated  resist- 
ance is  high.  For  example,  a platinum  film  5 cm.  long,  1 5 mm. 
wide  and  .0002  mm.  thick  has  a resistance  of  only  a few  ohms,  while 
a film  apparently  about  one  tenth  as  thick  1 has  a resistance  of  several 
hundred  ohms,  and  a film  probably  about  one  hundredth  as  thick, 
has  a resistance  of  hundreds  of  thousands  or  even  millions  of  ohms. 

There  is  plenty  of  room  for  further  investigation  in  this  direction, 
but  even  as  the  matter  stands,  it  seems  quite  unnecessary  to  use 
alloys  for  the  purpose  of  obtaining  high  specific  resistance. 

Quite  early  in  the  history  of  this  investigation  it  was  observed 
that  during  the  heating  and  cooling  of  certain  resistances,  for  the 
purpose  of  artificial  ageing,  the  resistance  changes  were  not  as  great 
as  the  temperature  changes  seemed  to  warrant,  and  in  one  note- 
worthy case  the  resistance  change  seemed  to  be  in  the  wrong  direc- 
tion. Accordingly,  the  temperature  coefficient  of  this  particular 
film  was  carefully  determined. 

This  film  was  deposited  April  4,  1 898.  During  the  preliminary 
treatment  for  bringing  it  to  a condition  of  stability,  its  resistance 
was  measured  quite  frequently.  The  measurements  were  made  at 
temperatures  differing  by  a few  degrees,  and,  even  during  the  first 
few  days,  while  the  changes  in  resistance  were  quite  large,  there  was 
at  least  an  indication  that  the  temperature  coefficient  was  probably 
negative. 

On  April  21st,  the  temperature  of  the  film  was  reduced  19  de- 
grees, and  the  reduced  temperature  was  kept  constant  for  several 
hours.  This  fall  of  temperature  was  accompanied  by  an  increase 
of  resistance  amounting  to  a little  more  than  6 ohms,  the  total  re- 
sistance of  the  film  being  a little  less  than  2,300,  though  it  had  not 
yet  reached  its  final  value.  When  the  temperature  of  the  film  was 
raised  to  its  former  value,  the  resistance  fell  about  4 ohms.  The 
discrepancy  between  the  6 ohms  rise  and  the  4 ohms  fall  was  due 
to  the  fact  that  the  process  of  artificial  ageing  was  not  yet  finished, 
but  there  was  no  longer  any  room  to  doubt  that  the  temperature 
coefficient  of  this  film  was  negative. 

1 Methods  of  determining  approximate  thickness  will  be  discussed  later. 


53 


A C.  LONG  DEN. 


[Vol.  XI. 


On  April  27th,  when  the  resistance  had  become  more  nearly 
constant,  this  film  was  provided  with  platinum  terminal  wires,  and 
sealed  into  a glass  tube  from  which  the  air  was  afterwards  ex- 
hausted to  about  .001  of  an  atmosphere,  the  tube  being  then  her- 
metically sealed. 

Its  record  on  the  last  three  days  of  the  month  was  as  follows  : 


Date. 

Apr.  28,  1898 
“ 29  “ 

“ 30  “ 


Temperature. 
23.2  degrees. 
2.0  “ 
23.1  “ 


Resistance. 

2284.1  ohms. 

2290.5  “ 

2284.2  “ 


The  temperature  coefficient  calculated  from  these  results  is 
— 0.00013. 

Even  at  the  date  of  these  measurements,  this  film  was  not  per- 
fectly seasoned,  but  the  subsequent  changes  in  resistance  were  very 
slight,  and  after  October  1,  1898,  no  changes  whatever  could  be 
detected  except  such  as  were  in  exact  harmony  with  the  above 
named  temperature  coefficient. 

In  November,  1898,  Mr.  F.  B.  Fawcett’s  very  interesting  article 
“On  Standard  High  Resistances”  appeared.1  In  this  article  Mr. 
Fawcett  points  out  the  early  rapid  decrease  in  the  resistance  of  a 
film  and  the  importance  of  artificial  ageing.  He  also  indicates  a 
method  of  standardizing  the  resistances  and  a method  of  artificial 
ageing ; but  in  determining  the  thickness  of  the  films,  he  assumes 
that  the  specific  resistance  is  the  same  for  all  films. 


The  Electrical  Contacts. 

In  these  experiments  for  a considerable  length  of  time  the  con- 
tacts between  the  films  and  their  terminal  wires  were  an  unfailing 
source  of  annoyance.  Clamps  were  used  at  first,  but  they  proved 
to  be  untrustworthy.  A piece  of  tin  foil  or  silver  foil  may  be  clamped 
to  a thick  film  and  the  contact  may  be  as  good  as  any  clamp  contact, 
which  is  not  saying  very  much.  Of  course  bright  metal  plates 
may  be  very  successfully  clamped  together  for  temporary  connec- 
tions, but  even  the  best  of  clamp  connections  can  hardly  be  con- 
sidered first  class  permanent  contacts  on  standard  resistances. 
Furthermore  if  a resistance  having  clamped  contacts  be  boiled  in  oil 
1 Phil.  Mag.,  5,  Vol.  46,  pp.  500-503. 


No.  i.] 


RESISTANCE  OF  THIN  FILMS. 


54 


or  paraffin  for  a number  of  hours,  as  in  the  process  of  artificial  age- 
ing, there  is  a strong  probability  that  the  insulating  material  will 
get  into  the  joints,  especially  if  the  coefficient  of  expansion  of  the 
clamp  is  greater  than  that  of  either  of  the  materials  held  together. 

Aside  from  all  this,  when  we  consider  making  contacts  with  a 
thin  film,  there  is  an  additional  difficulty.  These  films  are  rather 
delicate  and  will  not  endure  the  rough  usage  to  which  thick  films, 
wires  and  metal  plates  may  be  subjected.  If  the  slightest  crack  be 
produced  in  the  film,  by  the  pressure  of  the  clamp,  the  crack  will 
expand  and  contract  under  the  influence  of  temperature  changes, 
and  in  this  way  a variable  resistance  will  be  introduced  into  the 
circuit.  It  was  for  these  reasons  that  a number  of  attempts  were 
made,  several  of  which  resulted  in  perfectly  satisfactory  methods  of 
making  electrical  contacts  with  even  the  thinnest  of  the  films. 


The  first  attempt,  which  was  not  altogether  successful,  is  repre- 
sented in  figure  6.  ( AA ) are  strips  of  tin  foil  or  platinum  foil  fastened 
to  the  glass  with  shellac  varnish  and  thor- 
oughly baked.  The  film  ( B ) is  deposited 


C 

Fig'  6'  afterwards  over  the  entire  surface  of  glass  and 

foil,  and  if  thick  enough,  the  continuity  between  the  film  on  the  glass 
and  the  film  on  the  foil  is  perfect.  If,  however,  the  film  is  thin, 
there  is  lack  of  continuity  at  the  edge  of  the  foil.  The  method  may 
be  used  even  for  thin  films  by  covering  the  edge  of  the  foil  with  gold 
leaf  before  the  film  is  deposited.  This  makes  a joint  which  is  elec- 
trically good,  but  poor  mechanically. 

The  second  method  is  satisfactory  in  every  respect  and  is  appli- 
cable to  films  of  any  thickness.  This  method  is  represented  in  fig- 
ure 7.  In  this  case  the  film  is  deposited  first,  and  over  the  entire 
surface  of  the  glass.  The  receiver  is  then 
opened  and  the  portion  ( B ) of  the  film  is 
covered.  The  receiver  is  again  closed  and  ex- 
hausted and  the  deposition  of  metal  is  simply 
continued  until  the  portions  (AA)  are  very  thick.  We  then  have 
a continuous  film,  as  thin  as  we  please,  for  a high  resistance,  but 
with  ends  as  thick  as  we  please  for  making  connections.  The  fine 
copper  wires  (CC)  are  then  wound  on  and  permanently  secured  by 
electrolytic  deposition  of  copper  on  them. 


- — c c 

A 

B 

A 

Fig.  7. 


55 


A.  C.  LONG  DEN. 


[Vol.  XI. 


The  resulting  contact  leaves  absolutely  nothing  to  be  desired,  but 
the  process  is  rather  tedious.  A thin  film  may  be  produced  in  a 
few  minutes,  after  the  receiver  is  exhausted,  but  these  thick  ends  re- 
quire hours.  It  was  on  this  account  that  a third  method  was  de^ 
vised.  Figure  7 represents  this  method  as  well  as  the  preceding 
one.  In  this  case,  the  ends  of  the  glass  plates  are  first  immersed  in 
a silvering  solution,  and  thick  films  of  silver  (AA)  are  deposited 
upon  them  by  any  of  the  well-known  methods.  As  the  plate  stands 
in  the  silvering  bath  the  portion  which  is  below  the  plane  of  the  sur- 
face of  the  bath  becomes  heavily  coated  ; but  there  is  a small  area 
just  above  this  plane,  which  receives  silver  from  only  the  small 
amount  of  liquid  which  rises  above  the  plane  of  the  surface  of  the 
bath  by  capillary  action.  For  this  reason,  the  film,  however  thick 
it  may  be,  always  terminates  in  a very  thin  edge  so  that  the  film 
(i>),  which  is  afterwards  deposited  is  perfectly  continuous  over  the 
entire  surface  of  the  glass  and  silver.  The  copper  wires  ( CC ) are 
secured  in  this  case  in  the  same  way  as  in  the  preceding  case.  If 
the  silvering  of  the  ends  had  to  be  done  one  piece  at  a time,  this 
method  would  have  very  little  advantage  over  the  preceding  one, 
but,  as  a large  number  of  plates  may  be  placed  in  the  silvering  bath 
at  the  same  time,  the  amount  of  time  spent  in  silvering  the  ends  of 
the  plates  is  very  small. 

The  finished  film,  as  it  appears  in  figure  8,  "'j- 


Fig.  8. 


may  be  introduced  into  a Wheatstone  bridge 
circuit,  or  into  any  other  electric  circuit  for 
which  it  is  suitable,  just  as  if  it  were  a coil  of  wire.  It  has,  how- 
ever, the  advantages  of  being  non-inductive  and  practically  without 
capacity. 


(To  be  continued.) 


ELECTRICAL  RESISTANCE  OF  THIN  FILMS  DEPOSI- 
TED BY  KATHODE  DISCHARGE.  II.1 


By  A.  C.  Longden. 


The  Electrical  Measurements. 


HE  apparatus  used  in  making  the  tests  to  which  these  resist- 


ances  have  been  subjected  was  such  as  to  afford  results  of 
the  highest  attainable  accuracy ; and  in  all  cases  where  accuracy 
was  considered  important  no  painstaking  effort  has  been  spared  in 
securing  it. 

The  Wheatstone  bridge  and  rheostat  used  in  the  Ryerson  Labor- 
atory was  one  of  Queen’s,  of  the  kind  known  as  “ Set  No.  i,”  No.  80. 
The  rheostat  consists  of  five  sets  of  coils  aggregating  1 1,1 1 1 ohms, 
and  guaranteed  by  the  manufacturers  accurate  to  per  cent.  The 
bridge  is  provided  with  five  pairs  of  reversible  bridge  coils  ranging 
from  a pair  of  units  to  a pair  of  10,000  ohm  coils.  These  are 
guaranteed  accurate  to  per  cent.  The  temperature  of  the  coils 
was  determined  to  within  one  hundredth  of  a degree  by  means  of 
an  electrical  thermometer  placed  inside  of  the  box. 

Resistances  beyond  the  range  of  this  bridge  were  measured  by 
the  direct  deflection  method.  In  applying  this  method  a new  form 
of  water  battery2  devised  and  constructed  for  this  work  was  found 
useful,  convenient,  and  comparatively  inexpensive.  In  the  construc- 
tion of  this  battery,  instead  of  using  a copper  plate  and  a zinc  plate, 
two  copper  plates  are  used,  one  of  which  is  amalgamated  with  mer- 
cury containing  a little  zinc.  This  plate  presents  a zinc  surface  to 
the  water  and  is  therefore  equivalent  to  a zinc  plate  in  the  cell,  but 
it  does  not  dissolve  in  the  cell,  nor  become  brittle  and  break  off  at 
the  surface  of  the  water  as  an  all  zinc  plate  does.  The  resistance 
of  this  cell  may  be  varied  by  varying  its  size,  or,  within  certain 


1 Continued  from  page  55. 

2 Electrical  World,  Vol.  31,  p.  681. 


85 


A.  C.  LONG  DEN. 


[Vol.  XI. 


limits,  by  the  introduction  into  the  water  of  a small  quantity  (jL  of 
i per  cent.)  of  sulphuric  acid.  If  the  cell  is  properly  constructed 
and  sealed  it  requires  no  attention  whatever  for  many  months  at  a 
time,  and  its  electro-motive  force  is  practically  constant  as  long  as  it 
is  not  overworked.  Of  course  it  will  polarize  quite  rapidly  if  used 
on  anything  but  very  high  resistance  circuits.  It  is  not  intended  to 
furnish  much  current. 

In  the  work  done  at  Columbia  University,  for  measuring  resist- 
ances of  more  than  a few  thousand  ohms  it  was  found  convenient 
to  use  a bridge  of  the  slide-wire  type  in  which  a potentiometer  of 
100,000  ohms  forms  the  two  variable  resistances.  The  third  resist- 
ance was  the  one  under  test,  while  the  fourth  was  a standard  of 
10,000,  100,000  or  a i, 000,000  ohms.  The  rest  of  the  set  consisted 
of  a sensitive  Thomson  galvanometer  and  a battery  of  from  one  to 
one  hundred  dry  cells. 

The  potentiometer  used  was  designed  at  Columbia  University  by 
the  late  Mr.  Holbrook  Cushman,  and  was  constructed  for  the  uni- 
versity by  a mechanician  employed  for  the  purpose.  The  coils  were 
standardized  and  adjusted  at  the  University  by  Mr.  H.  C.  Parker 
and  his  assistants.  A fuller  description  of  the  instrument  is  given  in 
Mr.  Parker’s  admirable  work  on  Electrical  Measurements. 

The  10,000  and  100,000  ohm  standards  were  made  by  Elliott 
Bros,  of  London.  The  1,000,000  ohm  standard  was  one  of  the 
platinum  film  resistances  under  discussion,  but  its  resistance  was  fre- 
quently measured  and  it  was  found  to  be  perfectly  trustworthy. 

With  this  apparatus  a resistance  as  high  as  20  megohms  may  be 
measured  to  within  one  part  in  r 0,000. 

In  making  the  measurements  for  determining  temperature  coeffi- 
cients, the  standards  of  comparison  were  kept  in  the  electrical  test- 
ing room  in  the  Fayerweather  Laboratory.  The  resistances  under 
test  were  first  measured  in  that  room  at  the  same  temperature  as  the 
standards,  and  again  after  being  removed  to  an  underground  con- 
stant temperature  room,  located  just  outside  of  the  main  wall  of  the 
building,  and  entered  from  the  sub-basement.  One  arm  of  the 
bridge  in  the  testing  room  was  connected  with  a mercury  commu- 
tator in  the  underground  constant  temperature  room  by  a well  in- 
sulated, heavy  copper  wire  circuit  of  small  but  known  resistance. 


No.  2.] 


RESISTANCE  OF  THIN  FILMS. 


86 


For  all  high  resistance  work  this  circuit  is  negligible.  If  the  re- 
sistance to  be  measured  is  small  enough  to  make  it  at  all  important, 
the  resistance  of  the  line  is  deducted.  The  temperature  changes  in 
the  line  itself  are  very  slight,  but  of  course  the  method  is  not  used 
for  measuring  resistances  so  small  that  temperature  changes  in  the 
line  itself  would  produce  appreciable  errors  in  the  results. 

The  temperature  of  the  testing  room  is  ordinarily  about  20°  C., 
and  does  not  usually  vary  more  than  a degree  during  the  course  of 
a day.  The  temperature  of  the  underground  room  is  generally 
about  io°  or  n°  and  changes  very  slowly.  These  temperatures 
were  measured  by  means  of  well  seasoned  thermometers  which  have 
been  carefully  standardized  by  comparison  with  a thermometer  ac- 
companied by  a Reichsanstalt  certificate  dated  May  7,  1898. 

This  method  of  measuring  resistances  at  different  temperatures 
proved  to  be  at  once  convenient  and,  what  is  much  more  important, 
reliable.  Convenient,  because  no  special  precautions  were  neces- 
sary in  order  to  maintain  constant  temperatures,  and  reliable  be- 
cause there  could  be  no  doubt  about  the  temperature  of  a film  or 
coil  which  had  remained  undisturbed  in  a constant  temperature 
room  for  two  or  three  days. 

In  measuring  the  temperature  coefficients  of  film  resistances,  it 
was  soon  noted  that  all  of  the  very  thin  films  had  negative  tempera- 
ture coefficients,  while  all  of  the  thick  ones  had  positive  tempera- 
ture coefficients,  and  that  for  a certain  range  of  thicknesses  the 
temperature  coefficients  were  close  approximations  to  zero.  It  was 
also  noted  that,  unfortunately,  some  other  factor  besides  thickness 
enters  into  the  condition  which  produces  zero  temperature  coeffi- 
cients. This  other  factor  may  be,  and  probably  is,  density ; for 
this  is  obviously  the  most  variable  property  of  the  films.  When  it 
becomes  possible  to  hold  all  the  conditions  under  which  the  films 
are  deposited  in  perfect  control,  it  will,  doubtless,  be  possible  to 
produce  zero  temperature  coefficients  or  temperature  coefficients  of 
any  desired  value  by  simply  producing  films  of  certain  thicknesses. 
Even  under  present  conditions  the  range  of  thicknesses  for  negligible 
temperature  coefficients  is  not  small. 

Before  proceeding  further  with  this  part  of  the  subject  it  may  be 
well  to  state  that  for  convenience  a standard  length  and  breadth 


87 


A.  C.  LONG  DEN. 


[Vol.  XI. 


were  adopted  for  all  films,  so  that,  as  the  thickness  was  the  only 
varying  dimension,  its  relation  to  temperature  coefficients  might  the 
more  easily  be  discovered.  Therefore,  wherever  in  this  article 
films  are  in  any  way  compared,  it  may  be  assumed  that  they  are 
films  of  equal  length  and  breadth.  The  adopted  total  length  of  the 
glass  plate  is  7 cm.,  but  as  a centimeter  at  each  end  is  covered  with 
a thick  film  of  negligible  resistance  for  making  the  electrical  con- 
nections, the  length  of  the  ////>/ resistance  film  is  5 cm.  The  breadth 
is  in  all  cases  1 5 mm. 

A platinum  film  of  the  above  dimensions  thick  enough  to  have  a 
resistance  of  only  about  400  ohms,  has  a positive  temperature 
coefficient  equal  to  0.0003.  The  largest  negative  temperature 
coefficient  measured  was  — 0.005.  This  was  for  a film  so  thin  as  to 
have  a resistance  of  about  18  megohms.  If  the  curve  connecting 
temperature  coefficients  with  thickness,  were  a straight  line,  zero 
temperature  coefficients  would  occur  at  about  one  megohm,  for 
films  of  these  dimensions,  as  seen  by  the  position  of  the  dotted  line 
in  Figure  9.  As  a matter  of  fact,  however,  zero  or  negligible  tem- 


RISISTANCE  IN  MEGOHMS 


Fig.  9. 

perature  coefficients  frequently  occur  in  resistances  of  less  than 
5000  ohms,  and  they  occur  all  along  from  that  point  to  somewhere 
in  the  neighborhood  of  100,000  ohms.  It  must  also  be  remem- 
bered that  the  very  large  negative  coefficient  mentioned  above  is  an 
extreme  case.  The  large  number  of  results  indicated  by  the  points 
between  the  axis  of  ordinates  and  the  two-megohm  line  in  Figure 
9 indicates  that  for  films  of  a certain  density  the  real  position  of 
the  curve  is  probably  not  far  from  that  represented  in  the  figure. 
Fortunately  the  range  of  low  temperature  coefficients,  from  a few 
thousand  ohms  up  to  about  a megohm,  is  an  exceedingly  useful 


No.  2.] 


RESISTANCE  OF.  THIN  FILMS. 


88 


one.  It  could  hardly  have  happened  to  occur  in  a more  desirable 
place. 

Adjusting  and  Standardizing  Film  Resistances. 

It  is  important  to  consider  in  connection  with  the  question  of 
temperature  coefficients,  a method  of  adjusting  these  resistances  to 
a particular  value.  The  method  referred  to  is  substantially  the 
same  as  the  one  described  by  Mr.  Fawcett.  It  was  also  used  in 
this  investigation  as  early  as  June  2,  1898. 
It  consists  of  simply  cutting  the  film  into  sec- 
tions, as  in  Fig.  10,  so  as  to  increase  the  length 
and  diminish  the  breadth  of  the  conductor. 


Fig.  10. 


In  this  way  the  resistance  of  a film  may  easily  be  increased  ten  fold 
or  even  much  more  than  that,  if  necessary. 

Of  course  a resistance  may  in  this  way  be  adjusted  to  any  desired 
value,  provided  the  final  value  is  to  be  higher  than  the  original 
value  ; but  the  importance  of  the  method  in  connection  with  the 
question  of  temperature  coefficients  is  in  the  fact  that  a film  thin 
enough  to  have  a resistance  of  several  megohms  is  quite  likely  to 
have  a rather  large  negative  temperature  coefficient  (see  Fig.  9), 
while  a film  of  something  less  than  100,000  ohms  resistance  with 
a zero  or  negligible  temperature  coefficient  may,  by  means  of  the 
method  here  described,  have  its  resistance  increased  to  the  higher 
value  without  altering  its  temperature  coefficient. 

For  making  very  high  resistances  with  zero  temperature 
coefficients  it  is  advisable  to  use  wider  plates,  so  that  the 
current  may  be  made  to  traverse  the  length  of  the  plate  a 
greater  number  of  times  without  making  the  conductor 
dangerously  narrow. 

The  same  result  may  be  accomplished  by  bending  a small 
glass  tube  or  rod  into  the  form  shown  in  Fig.  1 1 and  de- 
positing upon  it  a film  of  such  thickness  as  to  have  a zero  Flg‘  U* 
or  neglible  temperature  coefficient.  In  this  case,  however,  the  final 
adjustment  to  a required  value  is  not  quite  so  easy. 

Aging  and  Protecting  the  Films. 

The  change  in  resistance  which  a film  undergoes,  quite  rapidly  at 
first,  and  less  rapidly  later,  makes  the  “ artificial  aging/’  or  “ sea- 


89 


A.  C.  LONG  DEN. 


[Vol.  XI. 


soning  ” process  one  of  great  importance.  There  are,  however,  no 
difficulties  connected  with  it.  It  is  the  same  process  for  films  as 
for  wire  resistances.  The  films  may  be  heated  and  cooled  in  the 
air,  or  they  may  be  boiled  in  oil  or  in  melted  paraffin.  In  any 
case  the  process  is  rather  a tedious  one  and  should  not  be  consid- 
ered at  an  end  until  sometime  after  the  point  has  been  reached 
where  no  further  change  is  noticeable.  Otherwise  the  resistance 
will  continue  to  undergo  slight  changes  for  a considerable  length 
of  time.  The  following  table  exhibits  some  of  the  results  of  per- 
fect and  imperfect  artificial  aging  : 


Resistance  in  Ohms. 

Class  A.  | 

1 

2265.8 

2265.7 

2265.8 

2265.8 

37586. 

37585. 

37588. 

37586. 

r 

3 

384.90 

383.72 

383.16 

382.92 

4 

9999.5 

9992.5 

9990.3 

9989.4 

Class  B. 

5 

15722. 

15697. 

15685. 

15681. 

1 

6 

23335. 

23680. 

23765. 

23774. 

l 

7 

165200. 

167680. 

167880. 

167930. 

( 

8 

84167. 

83710. 

83431. 

83178. 

Class  C.  1 

9 

656030. 

653600. 

651620. 

650110. 

l 

10 

4690000. 

5008000. 

5070000. 

5080000. 

The  values  given  in  the  successive  columns  are  for  measurements 
about  a month  apart,  and  either  made  at  the  same  temperature  or 
reduced  to  the  same  temperature  ; the  temperature  coefficients  of 
all  the  films  having  been  carefully  determined. 

The  films  in  class  (A)  were  thoroughly  seasoned ; while  those  in 
class  (B)  were  less  perfectly  seasoned  and  those  in  class  (C)  were 
very  poorly  seasoned.  It  will  be  observed  that  in  class  (C)  the  vari- 
ations amount  to  as  much  as  two  or  three  tenths  of  i per  cent,  even 
during  the  third  month.  In  class  (B)  the  corresponding  variations 
are  only  a few  hundredths  of  I per  cent.  ; while  in  class  (A)  no 
change  greater  than  could  be  attributed  to  errors  of  observation 
was  detected  during  the  entire  duration  of  the  test. 

In  subjecting  a number  of  films  to  the  process  of  artificial  ag- 
ing, a rather  important  relation  between  this  process  and  tempera- 
ture coefficients  was  observed.  By  keeping  the  films  connected  with 


No.  2.] 


RESISTANCE  OF  THIN  FILMS. 


90 


the  Wheatstone  bridge  during  the  aging  process,  it  was  seen  that 
the  resistances  did  not  continue  to  change  in  the  same  direction  dur- 
ing the  entire  process.  It  was  observed,  first,  that  if  the  rapid 
change  of  resistance  which  occurs  when  the  film  is  first  placed  in  a 
hot  bath  is  an  increase , it  will  soon  reach  a maximum  and  then 
gradually  decrease  for  a number  of  hours  ; second,  that  if  the  first 
rapid  change  is  a decrease , the  later  and  more  gradual  change  will 
be  an  increase  ; and  third,  that  if  the  resistance  does  not  change  at 
first  it  will  not  change  at  all.  Now  a film  of  the  first  kind  always 
has  a positive  temperature  coefficient,  while  one  of  the  second  kind 
always  has  a negative  temperature  coefficient.  Of  course  the  tem- 
perature coefficient  of  the  third  kind  is  zero. 

The  sign,  and  roughly  the  value  of  the  temperature  coefficient 
of  a film  resistance  may  be  determined  by  holding  a glowing  in- 
candescent lamp  within  about  an  inch  of  the  film,  while  the  latter 
forms  one  arm  of  a balanced  Wheatstone  bridge.  If  the  resistance 
does  not  change  at  all  the  temperature  coefficient  is  zero  and  the 
film  does  not  need  much  artificial  aging.  Briefly  stated,  the 
changes  in  resistance  which  occur  during  the  process  of  artificial 
aging,  and  the  length  of  time  required  to  bring  the  resistance  to  a 
permanent  value,  are  proportional  to  the  magnitude  of  the  tempera- 
ture coefficient.  Therefore  a low  temperature  coefficient  is  im- 
portant, not  only  for  its  own  sake,  but  also  as  a means  to  an  end. 
Films  having  low  temperature  coefficients  are  very  easily  seasoned 
and  extremely  reliable  after  seasoning. 

It  is  probably  true  that  in  films  there  are  not  as  many  causes 
at  work  to  create  a necessity  for  artificial  aging  as  in  the  case  of 
wires. 

It  has  recently  been  found  by  C.  de  Szily1  that  if  a wire  be  sub- 
jected to  torsion  its  electrical  resistance  increases,  and  that  if  the 
torsion  is  maintained  the  resistance  very  slowly  diminishes  with 
time.  Also  that  a wire,  which,  after  dextral  torsion,  has  been  re- 
lieved and  then  twisted  by  sinistral  torsion  to  the  zero  position, 
diminishes  in  resistance  more  quickly  that  when  the  twist  is  main- 
tained. Also  that  when  a wire  has  been  twisted  beyond  its  elastic 
limit,  and  has  been  allowed  to  untwist  itself,  subsequent  changes  of 
1 Comptes  Rendus,  Vol.  128,  pp.  927-930. 


91 


A.  C.  LONG  DEN. 


[Vol.  XI. 


resistance  for  torsion  • are  less  than  those  which  occur  during  the 
first  twist.  It  is  probable  that  stretching,  bending  and  even  wind- 
ing upon  a spool  all  produce  a similar  condition  in  wires. 

After  the  artificial  aging  process  is  at  an  end  it  is  important  that 
the  films  be  protected  from  the  air  in  order  that  no  new  conditions 
may  arise  to  produce  changes  in  resistance.  They  may  be  enclosed 
in  glass  tubes  from  which  the  air  is  exhausted,  they  may  be  simply 
imbedded  in  paraffin,  or  they  may  be  coated  with  varnish  prepared 
by  dissolving  India-rubber  in  carbon  bisulphide. 

Thickness  of  Films. 

In  consideration  of  the  relation  which  evidently  exists  between 
thickness  of  films  and  temperature  coefficients,  it  seems  desirable  to 
be  able  to  measure  the  thickness  of  the  films. 

It  is  to  be  regretted  that  no  method  of  making  an  exact  deter- 
mination of  the  thickness  of  the  very  thin  films  has  been  discovered. 
Miss  Stone  calculated  the  thickness  of  her  films  from  their  weighj 
and  area,  assuming  that  the  density  was  the  same  as  that  of  silver 
in  its  ordinary  condition.  However  correct  or  incorrect  this  method 
may  have  been  for  silver  films  deposited  from  aqueous  solutions,  it 
certainly  would  not  be  very  useful  in  determining  the  thickness  of 
films  of  such  varying  compactness  as  those  deposited  by  kathode 
discharge.  Furthermore,  many  of  the  films  considered  in  this  re- 
search are  entirely  too  thin  to  produce  any  impression  whatever 
upon  the  most  delicate  balance ; so  that  both  density  and  weight 
are  unknown  quantities.  Even  if  an  exact  determination  of  weight 
could  be  made,  it  would  be  of  doubtful  value,  because  of  the  vary- 
ing and  always  indefinite  amount  of  air  and  other  gases  absorbed  by 
the  film  and  weighed  with  it.  The  property  of  absorbing  and  oc- 
cluding gases  does  not  belong  to  platinum  alone.  It  is  possessed 
in  some  degree  by  a large  number  of  metals. 

For  this  and  other  reasons  it  was  deemed  desirable  to  attempt  to 
determine  the  weight  of  a few  films  by  the  methods  used  in  quanti- 
tative chemical  analysis.  Silver  was  the  metal  chosen  for  these  ex- 
periments, because  of  the  very  delicate  and  exact  existing  method 
for  its  quantitative  determination.  After  the  films  were  deposited, 
they  were  converted  into  silver  nitrate  and  then  subjected  to  the 


No.  2.] 


RESISTANCE  OF  THIN  FILMS. 


92 


volumetric  process  known  as  Gay-Lussac’s  method.  The  quantity 
of  silver  in  these  films  was  so  small  that  although  the  method  of 
analysis  used  was  the  one  which  Fresenius  describes  as  “ The  most 
exact  of  all  known  volumetric  processes,”  yet  it  was  not  possible  in 
any  case  to  make  an  exact  determination  of  the  amount  of  silver  in 
a transparent  film,  and  if  the  films  were  really  thin  it  was  not  even 
possible  to  detect  any  silver  in  the  solution.  These  facts  are  men- 
tioned as  forcible  illustrations  of  the  exceeding  thinness  of  the  films. 

The  assumption  upon  which  Mr.  Fawcett  bases  his  method  of 
calculating  thickness  is  certainly  unwarranted  ; for  in  very  thin  films, 
the  ratio  of  the  measured  resistance  to  the  calculated  resistance  is 
unquestionably  very  much  higher  than  it  is  in  thicker  films. 

Professor  Michelson’s  interferometer  furnishes  a direct  method  of 
measuring  the  thickness  of  comparatively  thick  films,  but  that  is 
not  the  important  part  of  the  problem ; for  even  a thick  film,  in  the 
sense  in  which  the  terms  thick  and  thin  are  here  used,  is  only  one 
or  two  tenths  of  a wave  length  thick.  However,  a few  compara- 
tive experiments  were  made  upon  thick  films,  determining  the 
thickness  by  means  of  the  interferometer  and  also  from  weight  and 
area.  In  some  cases  the  results  were  fairly  concordant,  indicating 
that  in  these  cases  the  density  was  about  normal. 

A silver  film  which  was  just  transparent  enough  to  reveal  the 
outline  of  a luminous  gas  jet  was  used  in  making  one  of  these  com- 
parisons. A portion  of  the  film  was  removed  from  the  glass  and 
the  optical  difference  of  path  between  the  surface  of  the  glass  and 
the  front  surface  of  the  film,  was  measured  by  means  of  the  inter- 
ferometer. The  displacement  of  the  interference  fringes  due  to  this 
difference  of  path  was  about  .3  of  a fringe.  (Sodium  light.)  The 
thickness  of  the  film  is  therefore  about  0.00009  mm-  The  thick- 
ness of  the  same  film,  calculated  from  its  weight,  0.0008  g.,  and 
area,  7.38  square  centimeters,  assuming  a density  of  10.55,  was 
0.00010  mm.  A platinum  film  somewhat  more  transparent  was 
found  by  the  interferometer  method  to  have  a thickness  of  0.00006 
mm.,  while  its  thickness,  calculated  from  its  weight  and  area  was 
0.000063  mm.  This,  however,  does  not  prove  that  the  density  of 
thin  films  is  the  same  as  that  of  thick  ones  or  even  that  the  density 
is  the  same  for  all  films  of  the  same  thickness. 


93 


A.  C.  LONGDEN. 


[Vol.  XI. 


It  must  be  remembered  that  both  of  the  films  just  considered 
were  thick  films.  The  utter  uselessness  of  attempting  to  weigh  very 
thin  films  is  illustrated  by  the  fact  that  a platinum  film  1 5 mm.  wide 
and  5 cm.  long,  weighing  only  0.00025  g.  has  a resistance  of  only 
about  2000  ohms.  What  would  be  the  weight  of  a film  thin  enough 
to  have  a resistance  of  several  megohms  ? 

Photometric  methods  are  of  some  service,  for  they  at  least  give 
an  indication  of  the  amount  of  metal  in  a film  which  is  too  thin  to 
be  weighed,  but  the  results  obtained  by  this  method  do  not  agree 
to  within  10  per  cent. 

There  is  yet  one  method  of  estimating  thickness  to  be  considered. 

It  seems  reasonable  to  suppose  that  the  rate  of  deposition  must 
be  uniform  under  uniform  conditions,  and  that  therefore  the  thick- 
nesses of  films  ought  to  be  directly  proportional  to  the  times  required 
for  their  deposition  ; provided  only  that  none  of  the  conditions  are 
allowed  to  change  during  the  process.  The  electro-motive  force, 
current  and  distance  are  under  perfect  control.  The  frequency  of 
the  Wehnelt  interrupter  is  not  very  difficult  to  control  if  the  tem- 
perature is  kept  constant  by  means  of  a cold  water  circulation. 
Even  the  vacuum  may  be  kept  within  reasonable  limits  if  very  great 
care  is  exercised  during  the  first  part  of  the  process,  while  the  oc- 
cluded gases  are  being  expelled.  It  is  therefore  believed  that  the 
time  element  in  the  deposition  of  a film  may  be  made  the  most  re- 
liable basis  for  estimating  thickness  ; and  it  is  this  element  that  has 
been  trusted  more  than  any  other  in  the  estimates  of  thickness  which 
have  been  made  during  the  progress  of  this  research. 

Choice  of  Materials. 

In  the  choice  of  a metal  for  the  production  of  film  resistances, 
permanence  has  been  the  chief  consideration,  and  platinum,  all  things 
considered,  is  believed  to  be  the  most  suitable  metal.  Gold  is 
doubtless  just  as  permanent  as  platinum  as  far  as  its  ability  to  resist 
chemical  action  is  concerned ; but  its  molecular  condition  does  not 
settle  down  to  a permanent  value  as  that  of  platinum  does.  H.  L. 
Callendar  in  his  work  “ On  a Practical  Thermometric  Standard  ” 1 
condemns  gold  as  a material  on  the  ground  that  there  is  a slow  but 

1 Phil*  Mag.,  S.  5,  Vol.  48,  pp.  519-547. 


No.  2.] 


R E SISTANCE  OF  THIN  FILMS. 


94 


constant  change  of  zero  in  a gold  thermometer.  This  of  course, 
means  a slow  but  constant  change  of  electrical  resistance  at  a cer- 
tain temperature.  It  is  for  this  reason  that  gold  is  not  a suitable 
metal  for  resistance  standards. 

A number  of  other  metals  have  been  experimented  upon,  but 
none  of  them  seemed  to  possess  any  advantage  over  platinum. 

Summary  of  Results. 

The  conclusions  drawn  from  this  investigation,  briefly  stated,  are 
as  follows  : 

(1)  The  process  of  depositing  metals  by  kathode  discharge  as 
illustrated  by  figures  3,  4 and  5,  is  probably  simple  distillation , in 
which  the  vaporization  of  the  kathode  is  largely  due  to  its  elec- 
trification. 

(2)  The  temperature  coefficients  of  the  very  thin  films  are  nega- 
tive, and  for  films  within  a certain  range  of  thicknesses,  the  tem- 
perature coefficients  are  approximately  zero. 

(3)  The  necessity  of  artificial  aging  is  proportional  to  the  mag- 
nitude of  the  temperature  coefficient. 

It  may  be  said  in  general  that  the  method  herein  described  is 
capable  of  producing  standard  electrical  resistances  of  a very  high 
degree  of  precision  and  of  any  desired  value,  from  a few  ohms  up 
to  several  megohms  ; that  these  resistances  may  be  made  of  pure 
metals — simple  elementary  substances — and  that  they  are  therefore 
free  from  the  possibility  of  decomposition  changes  ; that  the  metals 
may  be  those  least  likely  to  enter  into  chemical  combination  with 
other  elements  ; and  that  in  addition  to  these  valued  qualities  as 
pure  metals,  they  possess  the  only  desirable  qualities  of  alloys, 
namely  high  specific  resistance  and  low  temperature  coefficients. 

In  closing  this  dissertation  I wish  to  express  my  sincere  thanks  to 
Professors  Rood  and  Hallock,  of  Columbia  University,  for  their 
kindly  interest  in  my  work  and  for  the  many  helpful  suggestions 
which  they  have  given  me.  Also  to  Professors  Michelson  and 
Stratton,  of  the  University  of  Chicago,  for  valuable  assistance  during 
the  early  part  of  the  investigation. 

Fayerweather  Physical  Laboratory, 

Columbia  University,  March  31,  1900. 


